Distortionless Demodulation of Filtered Single-Sided Angle Modulation

In this paper the recovery of the modulation signal from filtered versions of single-sided angle modulation (SSBØM) by using a simple angle detector is investigated. A general analysis is made which suggests that for modulation signals of small amplitude and for relatively well behaved filters distortionless reception of the modulation signal is possible at the receiver if the angle detector is followed by an ideal low-pass filter. This result is proved for modulation signals which are band-limited and square-integrable functions of time, and for the pure sinusoid, when the modulated signals are ideally band limited. Of special practical and theoretical interest is the case where the ideally filtered SSBØM signal has the bandwidth saving of conventional single-sideband amplitude modulation (SSBAM). In this case a sufficient condition for distortionless reception of a signal
s(t)
with energy E
s
and one-sided bandwidth
W
is that
(2E_{s}W)^{1/2} < 0.8
, the maximum amplitude of the unmodulated carrier being 1. A necessary and sufficient condition for distortionless reception of the pure sinusoid
s(t) = d \cos w_{1)t
is:
d < 1
.